# If 2 power x = 3 power y = 6 power z , show that z = xy / x+y(pls ans within 20 mins because it is very urgent )

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by vikasvini

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by vikasvini

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2^x = 3^y = 6^z

2^x = 6^z

Raise both sides to power y.

* 2^{xy} = 6^{zy} -*-- (1)

3^y = 6^z

Raise both sides to power x

* 3^{xy} = 6^{xz} ---* (2)

multiply (1) and (2)

=> (2 * 3)^{x y} = 6^{z y + x z} = 6^{z(x+y)}

=> 6^{x y} = 6^{z(x+y)}

=> x y = z(x+y)

* => z = (x y) / (x + y)*

2^x = 6^z

Raise both sides to power y.

3^y = 6^z

Raise both sides to power x

multiply (1) and (2)

=> (2 * 3)^{x y} = 6^{z y + x z} = 6^{z(x+y)}

=> 6^{x y} = 6^{z(x+y)}

=> x y = z(x+y)